Generating function expectation

A probability distribution,[tex]f(x) [/tex] ,can be represented as a generating function,[tex]G(n) [/tex], as [tex] \sum_{x} f(x) n^x [/tex]. The expectation of [tex]f(x) [/tex] can be got from [tex] G'(1) [/tex].

Er, are you sure you're asking the right question? What meaning did you have in mind for "the expectation of f(x, y)"? Do you mean to think of f as the probability distribution for an R²-valued random variable, or something like that? Anyways, I would start by writing down the definition of expected value, and work from there.